Smaller interest area for images than the size of the image in classification neural networks
"The problem here is that if i use the whole image when training, my model will not learn that the interest area is only in the center of the image" Yes, it will, if you have enough samples and they are all classified based on this area only.

"but on the other hand if i crop the images to be of size 32x32 i am loosing a lot of information which can help the model to train on" . I don't understand what information you are loosing if you only care about the center 32x32 area.

In the end, you need to ask yourself how will the test input look like and work based on that. If you only care about an area of 32x32 which is always is (and will be) at the center of all images, ignore everything and train and evaluate based just on that area (why add extra unnecessary calculations to the model?). If the size and location of the area might change, don't crop the image.

Bottom line, the test set and the train set need to be of the nature (shape) for the model to work properly.